4 replies to this topic

[process16]

Hi

when we talk about pressure , velocity and flow of a liquide we have this theory:

flow of a liquide is the same at all points of a cylinder

and if pressure increase velocity should be decrease ...thats clear

what i don't understand :

for a same diameter in a pipe but after a pressure valve, pressure will decrease we know that

Q = V * S / Q : volumique flow, S : area ; V : velocity

so if Q , S are the same in different points A and B ( see the image )we have a contradiction because

V should be in the point B is greater than in the point A , ( pressure are lower in the point B )

could u explain that to me?

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[Francisco Angel]

Hi process 16:

I think the apparent contradiction arises because the general rule "if velocity increases, pressure decreases" is a consequence of an energy balance without dissipation of energy.

That rule doesn't apply if energy is removed (by the valve) or added to the system (with a pump, for example).

Consider the case of equal pipe diameters before and after a pump, in this case, you will have equal velocities at suction and discharge, but different pressures, because of the energy added to the fluid by the pump.

Best regards.

[samayaraj]

Hi Process16,

 

As you said, flow Q at A & B are same, for a identical cross section, velocity will remain same. Also refer the below link.

 

http://www.cheresour...e/#entry102808 

Edited by samayaraj, 27 April 2016 - 11:45 AM.

[shantanuk100]

Hi Process16,

 

1. Don't look at it just based on a proportionality between Pressure and Velocity. Go to the roots and see what concept that formula comes from. Let me explain.

 

2. The fundamental thing in this case is two things (assuming the fluid to be incompressible) :

 - First we conserve Mass by an equation called the continuity equation

- Second we conserve Energy using the Bernoulli equation  (Assuming no losses which I will explain further)

 

3. Now, when we have pipe flow, the Mass flow across the system is conserved because what goes in has to come out (Since fluid is incompressible).

So we write Mass flow rate m(in) = mass flow rate m(out)

rho1 * V1 = rho2 * V2

 

4. Also rho1 = rho2 (Since fluid is incompressible)

So, Volumetric flow rate V1 = Volumetric flow rate V2

Therefore A1*v1 = A2 * v2, where A is area of pipe cross section and v is velocity in that pipe cross section

 

5. Now the from energy conservation, we get the bernoulli equation which states that :

Pressure Energy + Kinetic Energy + Potential Energy = Constant for a fluid across the system

 

6. So, we get 

P/rho + v^2/ 2g + gH = Constant

Where P = fluid pressure in cross section, v=fluid velocity, g=gravitational acceleration, H=height of fluid section from reference

 

This statement means that any Difference in pressure across a system becomes the driving force for the fluid to move and thus indirectly the difference in pressure is what increases the velocity of a fluid. So as the velocity of the fluid increases , the pressure of the system decreases.

 

7. The above conservation of energy is valid only in systems where no energy is added / escapes externally.

But in our case, we have Turbulent flow, where we have swirling losses and eddy current losses which cause Energy to dissipate as noise and heat etc. to the surroundings

If we have same cross sectional areas, if we have A, C, B where Area of A=B and area of C is smaller than these, then, the velocity at C will be greater than A because area is smaller.

 

Irrespective of the pressure drop, the product of Area and Velocity is always constant, because the mass that goes in has to come out since the fluid is incompressible. But the pressure drop need not be exactly proportionally decreasing, because there are numerous factors like pipe friction, fluid viscosity, swirling and eddy currents that might cause different values of pressure drop.

 

Regards,

Shantanu

Edited by shantanuk100, 02 May 2016 - 11:34 PM.

[process16]

 thank you  all

i got it